How to correct Blender "physics visualization" inconsistancy with base mesh made of quads
It is always a bad idea to use quads... especially when it comes to games where you have physics and collision calculations. Everything will get converted to triangles anyway, for optimisation and accuracy purposes.
I couldn't exactly understand what the exact problem was, but whatever it is it would have something to do with the quads. 
Always triangulate before you use your mesh for simulation.
And if it is just because of this guys script that you keep a quad surface, then either edit the script that it takes in a triangulated mesh, or find a different LevelOfDetail (LOD) script.
PS: I am pretty sure he would be converting to trinagles somewhere in the script anyway, as it is not possible to get continuous LOD with quads